ORBITS SATELLITES IN ORBIT A satellite of the
ORBITS
SATELLITES IN ORBIT A satellite of the Earth, such as the moon, is constantly falling. But it does not fall towards the Earth, rather it falls around the Earth. Just as if you were in an elevator that was falling towards the Earth you would feel weightless if you were on an artificial satellite falling around the Earth.
THE SATELLITE EQUATION •
Example: A 4500 kg Earth satellite has an orbital radius of 8. 50 x 107 m. At what speed does it travel?
Example: A satellite orbits the Earth at a radius of 2. 20 x 107 m. What is its orbital period?
Geosynchronous Orbit The orbital speed of a satellite will depend on the strength of gravitational field at the orbital radius. Consider the following situations. Which identical satellite will be travelling faster in each. case? Why? 1) Satellite A orbits the Earth at twice the orbital radius of Satellite B. 2) Satellite A orbits the Sun at the same orbital radius that Satellite B orbits the Earth.
The orbital period of the satellite depends only on the mass of the planet and the orbital radius of the satellite. It stands to reason therefore that at a certain orbital distance the orbital period will match the rotational period of the planet. Such a satellite is said to be in geosynchronous (or geostationary) orbit.
Example: Find the orbital radius of a satellite that is geostationary above Earth’s equator. What is the speed of this satellite?
KEPLER’S LAWS OF PLANETARY MOTION • 1 st Law: The path of each planet about the Sun is an ellipse with the Sun at one focus.
KEPLER’S LAWS OF PLANETARY MOTION • 2 nd Law: Each planet moves so that an imaginary line drawn from the Sun to each planet sweeps out equal areas in equal periods of time.
KEPLER’S LAWS OF PLANETARY MOTION •
• KEPLER’S THIRD LAW
KEPLER’S LAWS • Note that these laws don not perfectly describe the motion of the planets about the Sun. • Since the planets are not only attracted to the Sun but also to each other, there will be perturbations from the predicted behaviour. • These perturbations helped Newton formulate his law of universal gravitation.
Example: A year on Mars is 687 days. How many times further is Mars from the Sun than the earth from the Sun?
- Slides: 15